scholarly journals A Fast Adaptive Algorithm Based on the Gradient Method and the Orthogonal Projection Matrix

1995 ◽  
Vol 115 (3) ◽  
pp. 345-353
Author(s):  
Toshihiro Furukawa ◽  
Tsunenori Maeda ◽  
Hajime Kubota
Keyword(s):  
Gradient Method ◽  
Orthogonal Projection ◽  
Adaptive Algorithm ◽  
Projection Matrix

Characterization of an orthogonal projection matrix

1993 ◽  
Vol 9 (3) ◽  
pp. 523-524
Author(s):  
R.W. Farebrother ◽  
P. Pordzik ◽  
G. Trenkler
Keyword(s):  
Orthogonal Projection ◽  
Projection Matrix

scholarly journals Semi-supervised Orthogonal Graph Embedding with Recursive Projections

2017 ◽  
Author(s):  
Hanyang Liu ◽  
Junwei Han ◽  
Feiping Nie
Keyword(s):  
Dimensionality Reduction ◽  
Orthogonal Projection ◽  
Graph Embedding ◽  
Feature Space ◽  
Linear Mapping ◽  
Projection Matrix ◽  
Data Matrix ◽  
Stiefel Manifold ◽  
Projection Direction ◽  
Number Of Classes

Many graph based semi-supervised dimensionality reduction algorithms utilize the projection matrix to linearly map the data matrix from the original feature space to a lower dimensional representation. But the dimensionality after reduction is inevitably restricted to the number of classes, and the learned non-orthogonal projection matrix usually fails to preserve distances well and balance the weight on different projection direction. This paper proposes a novel dimensionality reduction method, called the semi-supervised orthogonal graph embedding with recursive projections (SOGE). We integrate the manifold smoothness and label fitness as well as the penalization of the linear mapping mismatch, and learn the orthogonal projection on the Stiefel manifold that empirically demonstrates better performance. Moreover, we recursively update the projection matrix in its orthocomplemented space to continuously learn more projection vectors, so as to better control the dimension of reduction. Comprehensive experiment on several benchmarks demonstrates the significant improvement over the existing methods.

CONTROL OF SYNCHRONIZATION IN DELAY-COUPLED NETWORKS

2012 ◽  
Vol 26 (25) ◽  
pp. 1246007 ◽  
Author(s):  
E. SCHÖLL ◽  
A. SELIVANOV ◽  
J. LEHNERT ◽  
T. DAHMS ◽  
P. HÖVEL ◽  
...  
Keyword(s):  
Gradient Method ◽  
Adaptive Algorithm ◽  
Coupled Oscillators ◽  
Control Parameter ◽  
Phase Coupling ◽  
Cluster States ◽  
Phase Oscillation ◽  
Coupling Phase ◽  
Coupled Networks ◽  
Speed Gradient

We consider synchronization in networks of delay-coupled oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network, e.g., in-phase oscillation, splay or various cluster states. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase, coupling strength, and delay time such that a desired state can be selected from an otherwise multistable regime.

Characterization of an Orthogonal Projection Matrix

1995 ◽  
Vol 11 (3) ◽  
pp. 646-647
Author(s):  
R.W. Farebrother ◽  
Heinz Neudecker ◽  
Shuangzhe Liu
Keyword(s):  
Orthogonal Projection ◽  
Projection Matrix
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